2x2-7x=x2+15

Solution for 2x2-7x=x2+15 equation:

2x^2-7x=x2+15

We move all terms to the left:

2x^2-7x-(x2+15)=0

We add all the numbers together, and all the variables

2x^2-(+x^2+15)-7x=0

We get rid of parentheses

2x^2-x^2-7x-15=0

We add all the numbers together, and all the variables

x^2-7x-15=0

a = 1; b = -7; c = -15;
Δ = b2-4ac
Δ = -72-4·1·(-15)
Δ = 109
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{109}}{2*1}=\frac{7-\sqrt{109}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{109}}{2*1}=\frac{7+\sqrt{109}}{2}
$